import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
import scipy.stats
import statsmodels.api as sm
import numpy.ma as ma
import datetime as dt
import pingouin
data_1 = pd.read_excel("Regression 1.xlsx")
data_2 = pd.read_excel("Regression 2.xlsx")
data_3_1 = pd.read_excel("Regression 3-1.xlsx")
data_3_2 = pd.read_excel("Regression 3-2.xlsx")
#Test 1
## Processing the data
factors1 = ["Market Average Spread", "Rating", "Issuing Amount", "Tenor", "Green Indicator", "Russell ESG Score", "interaction"]
X1 = sm.add_constant(data_1[factors1])
model1 = sm.OLS(data_1["Coupon"], X1).fit()
# Fit the model
prediction1 = model1.predict(X1)
# Print the parameters of the fitted model
model1.summary()
| Dep. Variable: | Coupon | R-squared: | 0.834 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.829 |
| Method: | Least Squares | F-statistic: | 146.1 |
| Date: | Wed, 02 Nov 2022 | Prob (F-statistic): | 1.13e-75 |
| Time: | 12:06:02 | Log-Likelihood: | -38.813 |
| No. Observations: | 211 | AIC: | 93.63 |
| Df Residuals: | 203 | BIC: | 120.4 |
| Df Model: | 7 | ||
| Covariance Type: | nonrobust |
| coef | std err | t | P>|t| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| const | 0.1715 | 0.184 | 0.932 | 0.352 | -0.191 | 0.534 |
| Market Average Spread | 1.0509 | 0.065 | 16.193 | 0.000 | 0.923 | 1.179 |
| Rating | -0.1385 | 0.031 | -4.499 | 0.000 | -0.199 | -0.078 |
| Issuing Amount | -0.0031 | 0.002 | -1.533 | 0.127 | -0.007 | 0.001 |
| Tenor | 0.0355 | 0.022 | 1.601 | 0.111 | -0.008 | 0.079 |
| Green Indicator | -0.1127 | 0.134 | -0.841 | 0.401 | -0.377 | 0.152 |
| Russell ESG Score | 0.0790 | 0.043 | 1.860 | 0.064 | -0.005 | 0.163 |
| interaction | 0.0499 | 0.074 | 0.675 | 0.500 | -0.096 | 0.196 |
| Omnibus: | 110.439 | Durbin-Watson: | 1.225 |
|---|---|---|---|
| Prob(Omnibus): | 0.000 | Jarque-Bera (JB): | 1010.945 |
| Skew: | 1.792 | Prob(JB): | 2.99e-220 |
| Kurtosis: | 13.106 | Cond. No. | 198. |
## Obtaining the prediction and residual values
result1 = pd.concat([prediction1, model1.resid], axis =1)
result1 = result1.rename(columns = {0:'prediction', 1:'residual'})
## Print the regression results
with pd.option_context('display.max_rows', None,
'display.max_columns', None,
'display.precision', 3,
):
print(result1)
prediction residual 0 3.135 0.535 1 3.028 0.442 2 2.824 0.386 3 2.969 0.211 4 2.984 0.366 5 2.978 0.122 6 2.981 0.349 7 3.109 0.091 8 2.866 0.384 9 2.818 0.152 10 2.630 0.220 11 2.318 0.362 12 2.580 0.290 13 2.603 0.177 14 2.728 0.202 15 2.605 0.275 16 2.555 0.195 17 2.253 -0.253 18 2.650 -0.320 19 2.461 -0.211 20 2.296 -0.156 21 2.437 -0.207 22 2.201 0.029 23 2.296 -0.126 24 2.409 0.041 25 2.460 0.040 26 2.358 0.142 27 2.762 -0.162 28 2.286 -0.456 29 1.456 0.424 30 1.465 0.035 31 1.742 -0.132 32 1.739 -0.129 33 1.742 -0.132 34 1.612 -0.112 35 1.744 0.046 36 1.520 -0.050 37 1.726 -0.136 38 1.510 -0.010 39 1.947 -0.027 40 1.528 -0.048 41 1.536 -0.286 42 1.714 -0.214 43 1.691 -0.191 44 1.709 0.001 45 1.883 -0.333 46 1.644 -0.144 47 1.648 -0.148 48 1.650 -0.150 49 1.735 0.005 50 1.707 -0.207 51 1.509 -0.049 52 1.675 -0.175 53 1.689 0.061 54 1.682 -0.102 55 1.392 0.078 56 1.663 0.587 57 1.631 0.019 58 1.543 0.087 59 1.673 0.327 60 1.431 0.039 61 1.661 -0.011 62 1.561 -0.051 63 1.606 0.114 64 1.889 0.591 65 1.817 0.133 66 2.133 -0.273 67 1.878 0.122 68 1.940 -0.110 69 1.940 -0.110 70 2.193 0.307 71 1.935 0.065 72 1.884 0.116 73 2.054 -0.034 74 1.961 0.039 75 1.961 0.039 76 1.961 0.039 77 1.961 0.039 78 1.961 0.039 79 2.201 -0.161 80 2.432 -0.232 81 2.226 -0.226 82 2.195 -0.195 83 2.195 -0.195 84 2.611 -0.031 85 2.947 -0.747 86 2.384 -0.274 87 2.267 -0.097 88 2.339 -0.139 89 2.289 -0.289 90 2.289 -0.289 91 2.327 0.023 92 2.297 0.133 93 2.319 -0.089 94 2.605 0.245 95 2.895 0.005 96 3.516 -0.136 97 3.019 -0.069 98 3.615 -0.105 99 3.064 -0.114 100 3.624 -0.074 101 3.150 0.100 102 3.543 0.007 103 3.690 -0.060 104 2.663 0.087 105 2.761 0.039 106 2.831 0.239 107 3.526 -0.436 108 3.061 -0.261 109 2.982 -0.382 110 2.859 0.241 111 2.449 0.051 112 2.819 0.171 113 3.027 0.123 114 2.965 0.115 115 3.043 0.087 116 3.371 -0.121 117 2.844 -0.144 118 3.472 -0.072 119 2.995 0.055 120 2.962 -0.012 121 3.332 0.068 122 3.477 -0.027 123 2.655 0.045 124 3.521 -0.131 125 2.998 -0.048 126 2.835 0.065 127 3.249 0.071 128 3.614 -0.044 129 3.106 0.014 130 3.043 0.027 131 3.069 -0.009 132 2.553 -0.153 133 4.104 -0.404 134 3.003 -0.163 135 4.090 -0.350 136 3.059 0.011 137 3.064 -0.074 138 3.472 -0.122 139 3.755 -0.305 140 2.350 -0.210 141 2.653 -0.283 142 3.402 -0.202 143 3.570 -0.170 144 2.965 -0.365 145 3.251 -0.501 146 3.028 -0.198 147 2.804 -0.314 148 3.262 -0.132 149 3.407 -0.107 150 3.690 -0.240 151 2.726 -0.236 152 3.350 0.330 153 2.945 0.255 154 2.805 0.125 155 2.995 0.055 156 3.128 0.072 157 2.757 -0.107 158 2.898 -0.198 159 2.932 0.118 160 2.966 0.834 161 3.385 0.515 162 3.073 0.027 163 3.822 1.978 164 2.963 0.037 165 2.904 0.186 166 3.327 0.063 167 3.170 -0.210 168 3.353 0.227 169 2.903 0.547 170 2.838 0.612 171 3.419 0.731 172 2.927 0.373 173 2.912 1.028 174 2.669 -0.289 175 2.914 0.086 176 2.809 0.171 177 2.725 0.225 178 3.071 0.009 179 3.534 -0.014 180 3.687 0.073 181 2.535 0.665 182 2.581 0.319 183 2.707 0.293 184 3.711 -0.271 185 3.128 -0.038 186 2.911 -0.011 187 3.510 -0.110 188 3.580 -0.050 189 3.084 -0.284 190 2.837 -0.237 191 3.472 -0.032 192 3.022 0.098 193 3.478 -0.028 194 2.978 -0.138 195 3.868 -0.258 196 2.740 0.260 197 3.008 0.092 198 2.955 -0.275 199 2.647 -0.197 200 2.824 -0.024 201 3.069 -0.119 202 3.408 -0.208 203 2.935 -0.435 204 2.952 -0.762 205 3.043 -0.783 206 2.959 0.091 207 3.868 -0.068 208 3.543 -0.393 209 3.647 -0.397 210 3.656 0.054
## Show the regression in charts
for x in range(len(factors1)):
fig = plt.figure(figsize=(14, 8))
fig = sm.graphics.plot_regress_exog(model1,
factors1[x],
fig=fig)
eval_env: 1 eval_env: 1 eval_env: 1 eval_env: 1 eval_env: 1 eval_env: 1 eval_env: 1
## Anova test
pingouin.anova(data = data_1, dv = "Coupon", between = "Russell ESG Score")
| Source | ddof1 | ddof2 | F | p-unc | np2 | |
|---|---|---|---|---|---|---|
| 0 | Russell ESG Score | 17 | 193 | 2.850154 | 0.000255 | 0.200671 |
## Heatmaps
sns.heatmap(data_1.corr(), cmap='coolwarm', annot=True)
<AxesSubplot:>
# Test 2
## Processing the data
factors2 = ["overnight", "Refinitiv ESG Score", "rating", "Amount Issued (USD)", "Year", "interaction"]
X2 = sm.add_constant(data_2[factors2])
model2 = sm.OLS(data_2["Coupon"], X2).fit()
# Fit the model
prediction2 = model2.predict(X2)
# Print the parameters of the fitted model
model2.summary()
| Dep. Variable: | Coupon | R-squared: | 0.561 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.553 |
| Method: | Least Squares | F-statistic: | 67.73 |
| Date: | Wed, 02 Nov 2022 | Prob (F-statistic): | 5.76e-54 |
| Time: | 12:06:08 | Log-Likelihood: | -465.11 |
| No. Observations: | 325 | AIC: | 944.2 |
| Df Residuals: | 318 | BIC: | 970.7 |
| Df Model: | 6 | ||
| Covariance Type: | nonrobust |
| coef | std err | t | P>|t| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| const | 3.5240 | 0.346 | 10.193 | 0.000 | 2.844 | 4.204 |
| overnight | 1.5647 | 0.106 | 14.786 | 0.000 | 1.356 | 1.773 |
| Refinitiv ESG Score | -0.0078 | 0.004 | -1.764 | 0.079 | -0.017 | 0.001 |
| rating | -0.1565 | 0.028 | -5.644 | 0.000 | -0.211 | -0.102 |
| Amount Issued (USD) | 3.087e-10 | 2.02e-10 | 1.530 | 0.127 | -8.83e-11 | 7.06e-10 |
| Year | 0.0002 | 0.001 | 0.154 | 0.877 | -0.002 | 0.002 |
| interaction | -0.0042 | 0.008 | -0.538 | 0.591 | -0.020 | 0.011 |
| Omnibus: | 34.505 | Durbin-Watson: | 1.008 |
|---|---|---|---|
| Prob(Omnibus): | 0.000 | Jarque-Bera (JB): | 45.585 |
| Skew: | 0.754 | Prob(JB): | 1.26e-10 |
| Kurtosis: | 4.046 | Cond. No. | 4.32e+09 |
## Obtaining the prediction and residual values
result2 = pd.concat([prediction2, model2.resid], axis =1)
result2 = result2.rename(columns = {0:'prediction', 1:'residual'})
## Print the regression results
with pd.option_context('display.max_rows', None,
'display.max_columns', None,
'display.precision', 3,
):
print(result2)
prediction residual 0 3.254 1.121 1 1.959 -0.375 2 6.359 -1.234 3 3.372 1.378 4 6.107 -0.732 5 6.107 -0.732 6 6.020 -0.520 7 6.020 -0.520 8 3.203 1.547 9 3.194 0.306 10 2.916 0.209 11 3.118 0.595 12 3.264 1.611 13 2.669 0.456 14 2.760 0.115 15 3.367 1.133 16 5.712 0.541 17 5.712 0.541 18 3.094 0.031 19 2.653 3.347 20 2.176 1.074 21 4.721 0.404 22 4.734 0.641 23 5.337 -0.387 24 1.774 2.351 25 2.089 1.661 26 2.341 2.409 27 1.978 2.089 28 4.880 2.714 29 1.586 1.904 30 1.328 1.297 31 2.330 1.795 32 5.505 -0.755 33 6.601 -0.501 34 5.302 -1.152 35 6.111 -0.711 36 6.160 -0.560 37 1.993 0.882 38 4.728 1.103 39 4.728 1.103 40 4.700 1.836 41 4.700 1.836 42 1.102 3.398 43 4.169 -0.269 44 4.314 0.061 45 4.314 0.061 46 1.281 4.519 47 1.192 2.433 48 1.447 1.053 49 0.721 0.779 50 2.451 1.174 51 2.451 1.174 52 2.384 1.616 53 2.384 1.616 54 1.403 1.597 55 1.322 0.928 56 1.380 1.495 57 3.431 1.569 58 1.362 1.013 59 1.375 1.625 60 1.696 2.554 61 2.152 -1.528 62 1.369 0.881 63 1.305 1.195 64 1.612 0.513 65 1.187 2.063 66 0.674 1.451 67 1.622 1.128 68 2.095 -1.521 69 2.129 -1.485 70 1.540 0.585 71 1.147 1.103 72 3.385 1.240 73 3.385 1.240 74 0.918 1.332 75 1.208 0.917 76 2.979 1.271 77 0.792 0.958 78 1.052 0.867 79 0.414 0.649 80 2.014 -1.684 81 2.004 -1.430 82 0.702 0.923 83 3.071 0.829 84 1.352 0.648 85 1.657 1.093 86 1.495 -0.620 87 1.511 0.114 88 1.123 1.252 89 1.612 2.159 90 1.133 0.367 91 0.720 0.030 92 1.924 0.626 93 2.194 0.077 94 1.924 0.626 95 2.194 0.340 96 1.924 0.876 97 1.924 0.876 98 2.117 0.850 99 2.403 1.472 100 1.429 0.446 101 2.263 0.737 102 1.711 1.550 103 1.491 -0.116 104 1.233 -0.108 105 2.330 0.620 106 2.276 0.099 107 2.276 0.099 108 2.245 0.505 109 2.245 0.505 110 1.216 -0.466 111 1.623 -0.998 112 1.008 -0.133 113 2.481 -0.681 114 2.450 -0.200 115 2.999 0.571 116 2.999 0.571 117 2.152 0.420 118 2.152 0.420 119 2.511 0.339 120 1.704 -0.579 121 0.683 -0.308 122 1.536 -0.661 123 1.118 -0.368 124 1.780 0.692 125 3.305 0.445 126 3.305 0.445 127 3.305 0.445 128 1.741 -0.491 129 2.421 0.049 130 2.421 0.049 131 1.433 -1.183 132 1.264 -0.764 133 1.689 -0.689 134 1.566 -1.066 135 1.534 -0.534 136 1.489 -0.739 137 2.120 0.005 138 2.040 -0.140 139 0.416 -0.268 140 0.949 -0.199 141 1.739 -0.201 142 1.739 -0.201 143 3.437 -0.187 144 0.850 -0.600 145 2.086 -0.029 146 1.455 -0.455 147 2.716 -0.013 148 1.335 -0.960 149 1.353 -0.353 150 2.362 0.788 151 2.362 0.788 152 2.397 0.053 153 1.741 -1.116 154 1.754 -0.254 155 1.396 -0.271 156 1.402 1.913 157 1.463 -0.963 158 1.834 -0.034 159 2.269 1.231 160 2.269 1.231 161 2.565 -0.988 162 1.013 -0.888 163 2.133 -0.083 164 2.005 -0.130 165 2.080 -0.580 166 2.403 0.447 167 1.775 -0.400 168 1.569 -1.319 169 1.884 -0.509 170 2.514 -0.264 171 1.336 -0.961 172 1.797 -0.647 173 1.977 -0.852 174 1.960 -0.210 175 2.105 -0.755 176 2.358 -0.983 177 2.079 -0.704 178 2.079 -0.704 179 2.079 0.296 180 2.079 0.296 181 1.342 -0.542 182 1.285 -0.660 183 1.014 -0.139 184 2.104 0.796 185 1.341 -0.716 186 1.419 -1.044 187 1.749 -1.249 188 1.760 -0.510 189 1.526 -0.151 190 1.509 -0.884 191 1.442 -0.692 192 1.448 -0.573 193 2.177 -0.802 194 2.467 -0.967 195 1.419 -0.544 196 1.385 -0.260 197 1.413 -1.113 198 0.668 -0.418 199 1.222 -0.722 200 2.568 -0.068 201 3.230 1.020 202 1.447 -0.681 203 2.545 1.080 204 2.545 1.080 205 2.245 0.055 206 1.496 -0.121 207 2.190 -0.190 208 2.183 -1.183 209 2.183 -1.183 210 2.214 -0.464 211 2.214 -0.464 212 1.112 0.263 213 1.538 -0.938 214 1.125 -0.225 215 1.170 -1.124 216 1.862 -0.312 217 1.862 -0.312 218 1.934 0.441 219 1.186 -0.686 220 1.112 -0.612 221 1.815 -0.565 222 1.372 -0.622 223 1.156 -0.406 224 1.251 -0.876 225 0.825 -0.700 226 2.346 -1.221 227 1.758 -1.008 228 1.029 -1.019 229 2.331 -0.331 230 2.525 -0.025 231 0.416 -0.348 232 1.299 -1.299 233 1.656 -1.156 234 2.085 -0.210 235 1.464 -1.464 236 1.567 -1.317 237 2.529 -0.154 238 2.529 -0.154 239 1.826 -1.318 240 2.310 -0.410 241 1.350 -1.350 242 2.731 -1.356 243 2.731 -1.356 244 2.791 -0.341 245 2.791 -0.341 246 1.159 -1.149 247 1.512 -0.887 248 1.064 -1.064 249 2.437 -0.937 250 1.270 -1.145 251 1.661 -1.286 252 2.300 -0.600 253 1.631 -0.631 254 1.957 -1.007 255 1.206 -1.081 256 1.220 -0.845 257 2.598 -1.598 258 0.774 -0.560 259 1.751 0.749 260 2.582 -1.032 261 2.531 0.419 262 1.806 0.319 263 1.613 1.262 264 1.445 -0.695 265 2.043 1.207 266 1.532 -0.657 267 2.465 -0.965 268 2.365 0.260 269 2.365 0.260 270 2.457 -0.707 271 1.162 -0.412 272 1.388 -0.388 273 2.229 -0.379 274 1.934 -0.309 275 1.843 -1.093 276 1.791 1.159 277 1.417 -0.667 278 1.358 1.071 279 2.258 0.442 280 2.474 -1.074 281 2.474 -1.074 282 1.917 -0.042 283 2.364 -0.414 284 2.364 -0.114 285 1.371 -0.246 286 1.757 -0.717 287 1.417 -0.667 288 1.405 -1.030 289 1.519 -0.394 290 1.519 -0.394 291 0.777 0.598 292 1.180 -0.930 293 2.055 0.304 294 1.494 -0.619 295 1.758 0.992 296 1.680 -0.055 297 2.362 0.838 298 1.986 0.964 299 1.396 0.354 300 2.044 0.581 301 1.406 0.719 302 3.698 -2.198 303 1.330 -1.080 304 1.725 -0.350 305 1.537 -0.912 306 2.119 -0.419 307 1.649 -1.274 308 1.250 -0.500 309 1.243 -0.743 310 1.700 0.175 311 1.309 0.691 312 0.494 -0.494 313 1.222 -0.347 314 0.509 -0.009 315 4.461 -2.261 316 1.753 -0.128 317 1.421 -0.921 318 4.649 -2.599 319 1.342 -0.967 320 4.951 -1.851 321 4.411 -1.536 322 1.044 -0.744 323 3.077 -1.000 324 1.406 0.718
## Show the regression in charts
for x in range(len(factors2)):
fig = plt.figure(figsize=(14, 8))
fig = sm.graphics.plot_regress_exog(model2,
factors2[x],
fig=fig)
eval_env: 1 eval_env: 1 eval_env: 1 eval_env: 1 eval_env: 1 eval_env: 1
## Anova test
pingouin.anova(data = data_2, dv = "Coupon", between = "Refinitiv ESG Score")
| Source | ddof1 | ddof2 | F | p-unc | np2 | |
|---|---|---|---|---|---|---|
| 0 | Refinitiv ESG Score | 155 | 169 | 1.862813 | 0.000041 | 0.630792 |
## Heatmap
sns.heatmap(data_2.corr(), cmap='coolwarm', annot=True)
<AxesSubplot:>
# Test 3_1
## Processing the data
factors3_1 = ["Bloomberg ESG Score", "Credit Rating", "Risk free rate with same tenor", "Tenor", "Option"]
X3 = sm.add_constant(data_3_1[factors3_1])
model3_1 = sm.OLS(data_3_1["Coupon"], X3).fit()
# Fit the model
prediction3_1 = model3_1.predict(X3)
model3_1.summary()
| Dep. Variable: | Coupon | R-squared: | 0.780 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.747 |
| Method: | Least Squares | F-statistic: | 24.05 |
| Date: | Wed, 02 Nov 2022 | Prob (F-statistic): | 2.83e-10 |
| Time: | 12:06:14 | Log-Likelihood: | -45.347 |
| No. Observations: | 40 | AIC: | 102.7 |
| Df Residuals: | 34 | BIC: | 112.8 |
| Df Model: | 5 | ||
| Covariance Type: | nonrobust |
| coef | std err | t | P>|t| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| const | 1.5290 | 0.865 | 1.767 | 0.086 | -0.230 | 3.288 |
| Bloomberg ESG Score | 0.0071 | 0.015 | 0.487 | 0.630 | -0.023 | 0.037 |
| Credit Rating | -0.1530 | 0.066 | -2.310 | 0.027 | -0.288 | -0.018 |
| Risk free rate with same tenor | 1.0608 | 0.146 | 7.247 | 0.000 | 0.763 | 1.358 |
| Tenor | 0.0300 | 0.021 | 1.403 | 0.170 | -0.013 | 0.073 |
| Option | -0.1341 | 0.414 | -0.324 | 0.748 | -0.975 | 0.706 |
| Omnibus: | 2.534 | Durbin-Watson: | 1.691 |
|---|---|---|---|
| Prob(Omnibus): | 0.282 | Jarque-Bera (JB): | 2.359 |
| Skew: | 0.558 | Prob(JB): | 0.307 |
| Kurtosis: | 2.587 | Cond. No. | 365. |
## Obtaining the prediction and residual values
result3_1 = pd.concat([prediction3_1, model3_1.resid], axis =1)
result3_1 = result3_1.rename(columns = {0:'prediction', 1:'residual'})
## Print the regression results
with pd.option_context('display.max_rows', None,
'display.max_columns', None,
'display.precision', 3,
):
print(result3_1)
prediction residual 0 5.598 -0.648 1 5.236 0.864 2 4.806 1.730 3 4.156 -0.256 4 4.592 -0.217 5 4.945 0.930 6 4.872 -0.372 7 4.741 -0.491 8 4.493 0.132 9 4.992 1.133 10 2.835 -0.285 11 4.336 -0.461 12 2.916 -0.036 13 2.729 -0.929 14 3.283 -0.908 15 3.241 -0.941 16 4.673 -1.273 17 3.108 -0.837 18 4.114 -0.264 19 4.208 -0.583 20 2.326 -0.076 21 3.162 0.588 22 2.236 0.639 23 1.524 0.476 24 3.035 -0.535 25 3.087 -0.837 26 2.797 1.453 27 1.665 -0.790 28 4.215 0.535 29 1.690 -0.065 30 2.320 1.680 31 2.446 0.054 32 2.590 0.535 33 1.639 -0.014 34 0.601 0.852 35 0.285 -0.035 36 1.472 0.528 37 1.066 0.059 38 0.981 -0.356 39 1.226 -0.976
## Show the regression in charts
for x in range(len(factors3_1)):
fig = plt.figure(figsize=(14, 8))
fig = sm.graphics.plot_regress_exog(model3_1,
factors3_1[x],
fig=fig)
eval_env: 1 eval_env: 1 eval_env: 1 eval_env: 1 eval_env: 1
## Anova test
pingouin.anova(data = data_3_1, dv = "Coupon", between = "Bloomberg ESG Score")
/opt/anaconda3/lib/python3.9/site-packages/pingouin/parametric.py:1000: RuntimeWarning: invalid value encountered in double_scalars mserror = sserror / ddof2
| Source | ddof1 | ddof2 | np2 | |
|---|---|---|---|---|
| 0 | Bloomberg ESG Score | 39 | 0 | 1.0 |
## Heatmaps
sns.heatmap(data_3_1.corr(), cmap='coolwarm', annot=True)
<AxesSubplot:>
# Test 3_2
## Processing the data
factors3_2 = ["Market Average Spread", "Tenor", "Credit rating", "Issuer Type", "Russeel ESG Score"]
X3_2 = sm.add_constant(data_3_2[factors3_2])
model3_2 = sm.OLS(data_3_2["coupon"], X3_2).fit()
# Fit the model
prediction3_2 = model3_2.predict(X3_2)
# Print the parameters of the fitted model
model3_2.summary()
| Dep. Variable: | coupon | R-squared: | 0.786 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.766 |
| Method: | Least Squares | F-statistic: | 37.57 |
| Date: | Wed, 02 Nov 2022 | Prob (F-statistic): | 5.86e-16 |
| Time: | 12:06:18 | Log-Likelihood: | -8.2004 |
| No. Observations: | 57 | AIC: | 28.40 |
| Df Residuals: | 51 | BIC: | 40.66 |
| Df Model: | 5 | ||
| Covariance Type: | nonrobust |
| coef | std err | t | P>|t| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| const | 0.3724 | 0.470 | 0.792 | 0.432 | -0.572 | 1.316 |
| Market Average Spread | 1.6874 | 0.218 | 7.729 | 0.000 | 1.249 | 2.126 |
| Tenor | 0.0571 | 0.057 | 1.006 | 0.319 | -0.057 | 0.171 |
| Credit rating | -0.2621 | 0.045 | -5.829 | 0.000 | -0.352 | -0.172 |
| Issuer Type | -0.2458 | 0.043 | -5.773 | 0.000 | -0.331 | -0.160 |
| Russeel ESG Score | 0.0440 | 0.062 | 0.707 | 0.483 | -0.081 | 0.169 |
| Omnibus: | 3.346 | Durbin-Watson: | 1.702 |
|---|---|---|---|
| Prob(Omnibus): | 0.188 | Jarque-Bera (JB): | 2.471 |
| Skew: | 0.332 | Prob(JB): | 0.291 |
| Kurtosis: | 3.774 | Cond. No. | 85.1 |
## Obtaining the prediction and residual values
result3_2 = pd.concat([prediction3_2, model3_2.resid], axis =1)
result3_2 = result3_2.rename(columns = {0:'prediction', 1:'residual'})
## Print the regression results
with pd.option_context('display.max_rows', None,
'display.max_columns', None,
'display.precision', 3,
):
print(result3_2)
prediction residual 0 2.977 0.353 1 2.957 0.243 2 1.791 0.209 3 1.520 0.220 4 2.695 -0.195 5 2.205 -0.095 6 1.959 0.391 7 2.530 0.320 8 2.540 0.210 9 2.708 0.092 10 2.937 -0.137 11 2.642 -0.042 12 3.647 -0.547 13 3.075 0.175 14 2.645 0.055 15 3.292 0.108 16 2.915 0.135 17 2.883 0.067 18 3.159 0.241 19 3.430 0.020 20 2.917 0.143 21 3.358 -0.008 22 3.465 -0.015 23 2.135 0.005 24 2.451 -0.081 25 3.049 -0.449 26 3.023 -0.273 27 3.166 -0.336 28 2.918 -0.428 29 3.321 -0.121 30 2.608 0.042 31 3.001 -0.301 32 2.889 0.161 33 3.834 0.066 34 3.096 0.004 35 4.902 0.898 36 2.916 0.084 37 3.043 0.047 38 3.432 -0.042 39 3.590 -0.010 40 3.221 0.079 41 3.282 0.658 42 2.702 -0.322 43 2.883 0.317 44 2.897 0.003 45 3.120 -0.120 46 2.809 -0.009 47 3.032 -0.432 48 2.490 0.350 49 4.070 -0.460 50 2.551 0.129 51 2.434 0.016 52 2.857 -0.357 53 2.581 -0.391 54 2.729 -0.469 55 3.376 -0.326 56 3.585 0.125
## Show the regression in charts
for x in range(len(factors3_2)):
fig = plt.figure(figsize=(14, 8))
fig = sm.graphics.plot_regress_exog(model3_2,
factors3_2[x],
fig=fig)
eval_env: 1 eval_env: 1 eval_env: 1 eval_env: 1 eval_env: 1
## Anova test
print(pingouin.anova(data = data_3_2, dv = "coupon", between = "Russeel ESG Score"))
print(pingouin.anova(data = data_3_2, dv = "coupon", between = "Issuer Type"))
Source ddof1 ddof2 F p-unc np2
0 Russeel ESG Score 17 39 0.733641 0.750581 0.242305
Source ddof1 ddof2 F p-unc np2
0 Issuer Type 4 52 3.218563 0.019578 0.198449
## Heatmaps
sns.heatmap(data_3_2.corr(), cmap='coolwarm', annot=True)
<AxesSubplot:>
